Help Needed !

Two days ago a friend of mine shared with me a question stating that I couldn't solve that question and neither will anyone on Brilliant .

Darn him ! But he turned out to be partially correct , since I wasn't able to solve it and hence I am appealing to all the Brilliant minds out here to lend me your hand in solving the following question :

$\displaystyle \huge \sum_{r=1}^{\infty} \sqrt{ \int_{0}^{\frac{\pi}{2}} \left ( 5+ \Gamma \left ( \dfrac{2}{2+x^{2r}} \right ) \right ) dx}$

P.S. I tried using the Weirerstrass form and stuff , but was unsuccessful . I even posted this question in 3 communities in Google Plus , ends up that they got scared after seeing this question !

Best of Luck !!!

#Calculus #DefiniteIntegral #Summation #Challenge #GammaFunction

Easy Math Editor

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Comments

Is this gamma function, because if that is gamma function, then this sum doesn't converge.

Ronak Agarwal - 6 years, 3 months ago

Yeah, I also think so!

Kartik Sharma - 6 years, 3 months ago

Ok, sorry guys !! I didn't do the convergence test first !! I always forget to do it

A Former Brilliant Member - 6 years, 3 months ago

Can you please tell me something about that friend of yours, Is he studying in colledge, studying calculus. @Azhaghu Roopesh M

Ronak Agarwal - 6 years, 3 months ago

Actually he's also in Class 12 and it was he who gave me that Find it's closed form question .

A Former Brilliant Member - 6 years, 3 months ago

@Azhaghu Roopesh M , are you sure this question is solvable? Take it from a guy with experience, I once spent a whole day trying to prove Fermat's last theorem after my friend told me that I will never be able to solve it. Of course, I got to know that it was way out of my league the next day.

Raghav Vaidyanathan - 6 years, 3 months ago

Turns out the sum doesn't converge , sorry !!

Tell me more about your trying to prove the Last theo , now you've got me interested :D

A Former Brilliant Member - 6 years, 3 months ago

What's the claim that it converges?

Kartik Sharma - 6 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$